From 3eea0f7102214c7b770c79d9ab2c7fe3b7279a22 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Tue, 12 Mar 2024 12:41:12 +0800 Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=95E20250401=E6=96=B0=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v2/文本文件/新题收录列表.txt | 3 + 题库0.3/Problems.json | 166 ++++++++++++++++++++++++++++++- 2 files changed, 168 insertions(+), 1 deletion(-) diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index 46d27a1d..8a5d7b58 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -424,3 +424,6 @@ 20240311-162017 024722 +20240312-124031 高二下学期测验01 +041065,040956,041066,040958,041067:041072 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index a69e9492..3169cb5e 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -729059,7 +729059,9 @@ "20230730\t王伟叶" ], "same": [], - "related": [], + "related": [ + "041065" + ], "remark": "", "space": "", "unrelated": [] @@ -771730,5 +771732,167 @@ "remark": "", "space": "4em", "unrelated": [] + }, + "041065": { + "id": "041065", + "content": "若椭圆 $\\dfrac{x^2}{4}+\\dfrac{y^2}{2}=1$ 上一点 $P$ 到焦点 $F_1$ 的距离为 $3$, 则点 $P$ 到另外一个焦点 $F_2$ 的距离为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t杨懿荔" + ], + "same": [], + "related": [ + "031557" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "041066": { + "id": "041066", + "content": "若双曲线 $\\dfrac{x^2}{4}-\\dfrac{y^2}{b^2}=1$ 的右焦点为 $F(3,0)$, 则该双曲线的焦点到其渐近线的距离为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "041067": { + "id": "041067", + "content": "已知圆 $M:(x-3)^2+y^2=100, N(-3,0)$ . $P$ 是圆 $M$ 上的任意一点, 线段 $PN$ 的垂直平分线交线段 $PM$ 于 $Q$ 点, 则点 $Q$ 的轨迹方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "041068": { + "id": "041068", + "content": "双曲线 $\\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$) 的两渐近线夹角为 $2 \\arctan \\dfrac{3}{4}$, 若此双曲线实轴长为 8 ,则此双曲线焦距为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "041069": { + "id": "041069", + "content": "设 $F_1, F_2$ 是双曲线 $C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$) 的两个焦点, $P$ 是 $C$ 上一点, 若点 $P$ 满足: $|PF_1|+|PF_2|=6 a$, 且 $\\triangle PF_1F_2$ 的最小内角为 $30^{\\circ}$, 则双曲线 $C$ 的离心率为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "041070": { + "id": "041070", + "content": "已知椭圆 $\\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$) 的一条切线与 $x$、$y$ 轴分别交于点 $A$、$B$, 则 $\\triangle AOB$面积的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "041071": { + "id": "041071", + "content": "已知 $F_1, F_2$ 为椭圆 $C: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$) 的左, 右焦点, $M$ 为椭圆上的动点, 且$\\overrightarrow{MF_1}\\cdot \\overrightarrow{MF_2}$ 的最大值为 $1$, 最小值为$-2$.\\\\\n(1) 求椭圆 $C$ 的方程;\\\\\n(2) 过点 $(-\\dfrac{6}{5}, 0)$ 作不与 $y$ 轴垂直的直线 $l$ 交该制圆于 $M$、$N$ 两点, $A$ 为椭圆的左顶点,试判断 $\\angle MAN$ 是否为直角, 并说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "041072": { + "id": "041072", + "content": "已知双曲线 $C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$) 的左、右焦点分别为 $F_1$、$F_2$, 两顶点三等分焦距. 直线 $y=2$ 与 $C$ 的两个交点间的距离为 $\\sqrt{6}$.\\\\\n(1) 求 $a$、$b$ 的值;\\\\\n(2) 设过 $F_2$ 的直线 $l$ 与 $C$ 的左、右两支分别相交于 $A, B$ 两点,且 $|AF_1|=|BF_1|$, 证明: $|AF_2|$、$|AB|$、$|BF_2|$ 成等比数列.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240312\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] } } \ No newline at end of file